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Full Idea
The definition of a class or collection which enumerates is called a definition by 'extension', and one which mentions a defining property is called a definition by 'intension'.
Gist of Idea
A definition by 'extension' enumerates items, and one by 'intension' gives a defining property
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], II)
Book Ref
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.12
A Reaction
In ordinary usage we take intensional definitions for granted, so it is interesting to realise that you might define 'tiger' by just enumerating all the tigers. But all past tigers? All future tigers? All possible tigers which never exist?
| 16094 | You can't define particulars, because accounts have to be generalised [Aristotle] |
| 12983 | A nominal definition is of the qualities, but the real definition is of the essential inner structure [Leibniz] |
| 4417 | Only that which has no history is definable [Nietzsche] |
| 16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
| 14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell] |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| 11221 | A definition can be 'extensionally', 'intensionally' or 'sense' adequate [Gupta] |
| 11224 | Traditional definitions are general identities, which are sentential and reductive [Gupta] |
| 11226 | Traditional definitions need: same category, mention of the term, and conservativeness and eliminability [Gupta] |
| 9143 | Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Fine,K, by Cook/Ebert] |
| 10143 | 'Creative definitions' do not presuppose the existence of the objects defined [Fine,K] |